/*
 * Copyright (c) 1994, 2020, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
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 */

package java.lang;

import java.lang.annotation.Native;

/**
 * {@code Integer} 类在对象中包装了一个基本类型 {@code int} 的值。
 * {@code Integer} 类型的对象包含一个 {@code int} 类型的字段。
 *
 * <p>此外，该类提供了多个方法，用于将 {@code int} 转换为 {@code String}，
 * 将 {@code String} 转换为 {@code int}，以及处理 {@code int} 时有用的
 * 其他常量和方法。
 *
 * <p>实现注意事项："位操作"方法（如 {@link #highestOneBit(int) highestOneBit} 和
 * {@link #numberOfTrailingZeros(int) numberOfTrailingZeros}）的实现
 * 基于 Henry S. Warren, Jr. 的 <i>Hacker's Delight</i>（Addison Wesley, 2002）中的材料。
 *
 * @author  Lee Boynton
 * @author  Arthur van Hoff
 * @author  Josh Bloch
 * @author  Joseph D. Darcy
 * @since JDK1.0
 */
public final class Integer extends Number implements Comparable<Integer> {
    /**
     * 保存 {@code int} 类型可以拥有的最小值的常量，-2<sup>31</sup>。
     */
    @Native public static final int   MIN_VALUE = 0x80000000;

    /**
     * 保存 {@code int} 类型可以拥有的最大值的常量，2<sup>31</sup>-1。
     */
    @Native public static final int   MAX_VALUE = 0x7fffffff;

    /**
     * 表示基本类型 {@code int} 的 {@code Class} 实例。
     *
     * @since   JDK1.1
     */
    @SuppressWarnings("unchecked")
    public static final Class<Integer>  TYPE = (Class<Integer>) Class.getPrimitiveClass("int");

    /**
     * 用于将数字表示为字符串的所有可能字符
     */
    final static char[] digits = {
        '0' , '1' , '2' , '3' , '4' , '5' ,
        '6' , '7' , '8' , '9' , 'a' , 'b' ,
        'c' , 'd' , 'e' , 'f' , 'g' , 'h' ,
        'i' , 'j' , 'k' , 'l' , 'm' , 'n' ,
        'o' , 'p' , 'q' , 'r' , 's' , 't' ,
        'u' , 'v' , 'w' , 'x' , 'y' , 'z'
    };

    /**
     * 返回第一个参数在第二个参数指定的基数中的字符串表示形式。
     *
     * <p>如果基数小于 {@code Character.MIN_RADIX} 或大于 {@code Character.MAX_RADIX}，
     * 则使用基数 {@code 10}。
     *
     * <p>如果第一个参数为负数，则结果的第一个元素是 ASCII 减号字符 {@code '-'}
     * ({@code '\u005Cu002D'})。如果第一个参数不是负数，则结果中不出现符号字符。
     *
     * <p>结果的其余字符表示第一个参数的大小。如果大小为零，则用单个零字符 {@code '0'}
     * ({@code '\u005Cu0030'}) 表示；否则，大小表示的第一个字符不会是零字符。
     * 以下 ASCII 字符用作数字：
     *
     * <blockquote>
     *   {@code 0123456789abcdefghijklmnopqrstuvwxyz}
     * </blockquote>
     *
     * 这些是从 {@code '\u005Cu0030'} 到 {@code '\u005Cu0039'} 和从 {@code '\u005Cu0061'}
     * 到 {@code '\u005Cu007A'}。如果 {@code radix} 是 <var>N</var>，则按所示顺序使用
     * 这些字符的前 <var>N</var> 个作为基数-<var>N</var> 数字。因此，十六进制（基数 16）
     * 的数字是 {@code 0123456789abcdef}。如果需要大写字母，可以对结果调用
     * {@link java.lang.String#toUpperCase()} 方法：
     *
     * <blockquote>
     *  {@code Integer.toString(n, 16).toUpperCase()}
     * </blockquote>
     *
     * @param   i       要转换为字符串的整数。
     * @param   radix   字符串表示中使用的基数。
     * @return  指定基数中参数的字符串表示形式。
     * @see     java.lang.Character#MAX_RADIX
     * @see     java.lang.Character#MIN_RADIX
     */
    public static String toString(int i, int radix) {
        if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
            radix = 10;

        /* Use the faster version */
        if (radix == 10) {
            return toString(i);
        }

        char buf[] = new char[33];
        boolean negative = (i < 0);
        int charPos = 32;

        if (!negative) {
            i = -i;
        }

        while (i <= -radix) {
            buf[charPos--] = digits[-(i % radix)];
            i = i / radix;
        }
        buf[charPos] = digits[-i];

        if (negative) {
            buf[--charPos] = '-';
        }

        return new String(buf, charPos, (33 - charPos));
    }

    /**
     * 返回第一个参数作为无符号整数值在第二个参数指定的基数中的字符串表示形式。
     *
     * <p>如果基数小于 {@code Character.MIN_RADIX} 或大于 {@code Character.MAX_RADIX}，
     * 则使用基数 {@code 10}。
     *
     * <p>请注意，由于第一个参数被视为无符号值，因此不会打印前导符号字符。
     *
     * <p>如果大小为零，则用单个零字符 {@code '0'} ({@code '\u005Cu0030'}) 表示；
     * 否则，大小表示的第一个字符不会是零字符。
     *
     * <p>基数的行为和用作数字的字符与 {@link #toString(int, int) toString} 相同。
     *
     * @param   i       要转换为无符号字符串的整数。
     * @param   radix   字符串表示中使用的基数。
     * @return  指定基数中参数的无符号字符串表示形式。
     * @see     #toString(int, int)
     * @since 1.8
     */
    public static String toUnsignedString(int i, int radix) {
        return Long.toUnsignedString(toUnsignedLong(i), radix);
    }

    /**
     * 返回整数参数作为无符号整数在十六进制（基数&nbsp;16）中的字符串表示形式。
     *
     * <p>如果参数为负数，则无符号整数值为参数加上 2<sup>32</sup>；
     * 否则等于参数。此值被转换为十六进制（基数&nbsp;16）的 ASCII 数字字符串，
     * 没有额外的前导 {@code 0}。
     *
     * <p>可以通过调用 {@link Integer#parseUnsignedInt(String, int)
     * Integer.parseUnsignedInt(s, 16)} 从返回的字符串 {@code s} 中恢复参数的值。
     *
     * <p>如果无符号大小为零，则用单个零字符 {@code '0'} ({@code '\u005Cu0030'})
     * 表示；否则，无符号大小表示的第一个字符不会是零字符。
     * 以下字符用作十六进制数字：
     *
     * <blockquote>
     *  {@code 0123456789abcdef}
     * </blockquote>
     *
     * 这些是从 {@code '\u005Cu0030'} 到 {@code '\u005Cu0039'} 和从
     * {@code '\u005Cu0061'} 到 {@code '\u005Cu0066'} 的字符。
     * 如果需要大写字母，可以对结果调用 {@link java.lang.String#toUpperCase()} 方法：
     *
     * <blockquote>
     *  {@code Integer.toHexString(n).toUpperCase()}
     * </blockquote>
     *
     * @param   i   要转换为字符串的整数。
     * @return  参数在十六进制（基数&nbsp;16）中表示的无符号整数值的字符串表示形式。
     * @see #parseUnsignedInt(String, int)
     * @see #toUnsignedString(int, int)
     * @since   JDK1.0.2
     */
    public static String toHexString(int i) {
        return toUnsignedString0(i, 4);
    }

    /**
     * 返回整数参数作为无符号整数在八进制（基数&nbsp;8）中的字符串表示形式。
     *
     * <p>如果参数为负数，则无符号整数值为参数加上 2<sup>32</sup>；
     * 否则等于参数。此值被转换为八进制（基数&nbsp;8）的 ASCII 数字字符串，
     * 没有额外的前导 {@code 0}。
     *
     * <p>可以通过调用 {@link Integer#parseUnsignedInt(String, int)
     * Integer.parseUnsignedInt(s, 8)} 从返回的字符串 {@code s} 中恢复参数的值。
     *
     * <p>如果无符号大小为零，则用单个零字符 {@code '0'} ({@code '\u005Cu0030'})
     * 表示；否则，无符号大小表示的第一个字符不会是零字符。
     * 以下字符用作八进制数字：
     *
     * <blockquote>
     * {@code 01234567}
     * </blockquote>
     *
     * 这些是从 {@code '\u005Cu0030'} 到 {@code '\u005Cu0037'} 的字符。
     *
     * @param   i   要转换为字符串的整数。
     * @return  参数在八进制（基数&nbsp;8）中表示的无符号整数值的字符串表示形式。
     * @see #parseUnsignedInt(String, int)
     * @see #toUnsignedString(int, int)
     * @since   JDK1.0.2
     */
    public static String toOctalString(int i) {
        return toUnsignedString0(i, 3);
    }

    /**
     * 返回整数参数作为无符号整数在二进制（基数&nbsp;2）中的字符串表示形式。
     *
     * <p>如果参数为负数，则无符号整数值为参数加上 2<sup>32</sup>；
     * 否则等于参数。此值被转换为二进制（基数&nbsp;2）的 ASCII 数字字符串，
     * 没有额外的前导 {@code 0}。
     *
     * <p>可以通过调用 {@link Integer#parseUnsignedInt(String, int)
     * Integer.parseUnsignedInt(s, 2)} 从返回的字符串 {@code s} 中恢复参数的值。
     *
     * <p>如果无符号大小为零，则用单个零字符 {@code '0'} ({@code '\u005Cu0030'})
     * 表示；否则，无符号大小表示的第一个字符不会是零字符。
     * 字符 {@code '0'} ({@code '\u005Cu0030'}) 和 {@code '1'} ({@code '\u005Cu0031'})
     * 用作二进制数字。
     *
     * @param   i   要转换为字符串的整数。
     * @return  参数在二进制（基数&nbsp;2）中表示的无符号整数值的字符串表示形式。
     * @see #parseUnsignedInt(String, int)
     * @see #toUnsignedString(int, int)
     * @since   JDK1.0.2
     */
    public static String toBinaryString(int i) {
        return toUnsignedString0(i, 1);
    }

    /**
     * Convert the integer to an unsigned number.
     */
    private static String toUnsignedString0(int val, int shift) {
        // assert shift > 0 && shift <=5 : "Illegal shift value";
        int mag = Integer.SIZE - Integer.numberOfLeadingZeros(val);
        int chars = Math.max(((mag + (shift - 1)) / shift), 1);
        char[] buf = new char[chars];

        formatUnsignedInt(val, shift, buf, 0, chars);

        // Use special constructor which takes over "buf".
        return new String(buf, true);
    }

    /**
     * Format a long (treated as unsigned) into a character buffer.
     * @param val the unsigned int to format
     * @param shift the log2 of the base to format in (4 for hex, 3 for octal, 1 for binary)
     * @param buf the character buffer to write to
     * @param offset the offset in the destination buffer to start at
     * @param len the number of characters to write
     * @return the lowest character  location used
     */
     static int formatUnsignedInt(int val, int shift, char[] buf, int offset, int len) {
        int charPos = len;
        int radix = 1 << shift;
        int mask = radix - 1;
        do {
            buf[offset + --charPos] = Integer.digits[val & mask];
            val >>>= shift;
        } while (val != 0 && charPos > 0);

        return charPos;
    }

    final static char [] DigitTens = {
        '0', '0', '0', '0', '0', '0', '0', '0', '0', '0',
        '1', '1', '1', '1', '1', '1', '1', '1', '1', '1',
        '2', '2', '2', '2', '2', '2', '2', '2', '2', '2',
        '3', '3', '3', '3', '3', '3', '3', '3', '3', '3',
        '4', '4', '4', '4', '4', '4', '4', '4', '4', '4',
        '5', '5', '5', '5', '5', '5', '5', '5', '5', '5',
        '6', '6', '6', '6', '6', '6', '6', '6', '6', '6',
        '7', '7', '7', '7', '7', '7', '7', '7', '7', '7',
        '8', '8', '8', '8', '8', '8', '8', '8', '8', '8',
        '9', '9', '9', '9', '9', '9', '9', '9', '9', '9',
        } ;

    final static char [] DigitOnes = {
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        '0', '1', '2', '3', '4', '5', '6', '7', '8', '9',
        } ;

        // I use the "invariant division by multiplication" trick to
        // accelerate Integer.toString.  In particular we want to
        // avoid division by 10.
        //
        // The "trick" has roughly the same performance characteristics
        // as the "classic" Integer.toString code on a non-JIT VM.
        // The trick avoids .rem and .div calls but has a longer code
        // path and is thus dominated by dispatch overhead.  In the
        // JIT case the dispatch overhead doesn't exist and the
        // "trick" is considerably faster than the classic code.
        //
        // TODO-FIXME: convert (x * 52429) into the equiv shift-add
        // sequence.
        //
        // RE:  Division by Invariant Integers using Multiplication
        //      T Gralund, P Montgomery
        //      ACM PLDI 1994
        //

    /**
     * 返回表示指定整数的 {@code String} 对象。参数被转换为有符号十进制表示形式
     * 并作为字符串返回，就像将参数和基数 10 作为参数传递给 {@link #toString(int, int)} 方法一样。
     *
     * @param   i   要转换的整数。
     * @return  参数在十进制（基数&nbsp;10）中的字符串表示形式。
     */
    public static String toString(int i) {
        if (i == Integer.MIN_VALUE)
            return "-2147483648";
        int size = (i < 0) ? stringSize(-i) + 1 : stringSize(i);
        char[] buf = new char[size];
        getChars(i, size, buf);
        return new String(buf, true);
    }

    /**
     * 返回参数作为无符号十进制值的字符串表示形式。
     *
     * 参数被转换为无符号十进制表示形式并作为字符串返回，
     * 就像将参数和基数 10 作为参数传递给 {@link #toUnsignedString(int, int)} 方法一样。
     *
     * @param   i  要转换为无符号字符串的整数。
     * @return  参数的无符号字符串表示形式。
     * @see     #toUnsignedString(int, int)
     * @since 1.8
     */
    public static String toUnsignedString(int i) {
        return Long.toString(toUnsignedLong(i));
    }

    /**
     * 将表示整数 i 的字符放入字符数组 buf 中。字符从指定索引（不包括）
     * 处的最低有效数字开始向后放入缓冲区，然后从那里向后工作。
     *
     * 如果 i == Integer.MIN_VALUE 将失败
     */
    static void getChars(int i, int index, char[] buf) {
        int q, r;
        int charPos = index;
        char sign = 0;

        if (i < 0) {
            sign = '-';
            i = -i;
        }

        // Generate two digits per iteration
        while (i >= 65536) {
            q = i / 100;
        // really: r = i - (q * 100);
            r = i - ((q << 6) + (q << 5) + (q << 2));
            i = q;
            buf [--charPos] = DigitOnes[r];
            buf [--charPos] = DigitTens[r];
        }

        // Fall thru to fast mode for smaller numbers
        // assert(i <= 65536, i);
        for (;;) {
            q = (i * 52429) >>> (16+3);
            r = i - ((q << 3) + (q << 1));  // r = i-(q*10) ...
            buf [--charPos] = digits [r];
            i = q;
            if (i == 0) break;
        }
        if (sign != 0) {
            buf [--charPos] = sign;
        }
    }

    final static int [] sizeTable = { 9, 99, 999, 9999, 99999, 999999, 9999999,
                                      99999999, 999999999, Integer.MAX_VALUE };

    // Requires positive x
    static int stringSize(int x) {
        for (int i=0; ; i++)
            if (x <= sizeTable[i])
                return i+1;
    }

    /**
     * 将字符串参数解析为第二个参数指定基数中的有符号整数。
     * 字符串中的字符必须都是指定基数的数字（由 {@link java.lang.Character#digit(char, int)}
     * 是否返回非负值确定），除了第一个字符可以是 ASCII 减号 {@code '-'}
     * ({@code '\u005Cu002D'}) 表示负值，或 ASCII 加号 {@code '+'}
     * ({@code '\u005Cu002B'}) 表示正值。返回结果整数值。
     *
     * <p>如果出现以下任何情况，将抛出 {@code NumberFormatException} 类型的异常：
     * <ul>
     * <li>第一个参数为 {@code null} 或长度为零的字符串。
     *
     * <li>基数小于 {@link java.lang.Character#MIN_RADIX} 或
     * 大于 {@link java.lang.Character#MAX_RADIX}。
     *
     * <li>字符串的任何字符都不是指定基数的数字，除了第一个字符可以是减号
     * {@code '-'} ({@code '\u005Cu002D'}) 或加号 {@code '+'}
     * ({@code '\u005Cu002B'})，前提是字符串长度大于 1。
     *
     * <li>字符串表示的值不是 {@code int} 类型的值。
     * </ul>
     *
     * <p>示例：
     * <blockquote><pre>
     * parseInt("0", 10) 返回 0
     * parseInt("473", 10) 返回 473
     * parseInt("+42", 10) 返回 42
     * parseInt("-0", 10) 返回 0
     * parseInt("-FF", 16) 返回 -255
     * parseInt("1100110", 2) 返回 102
     * parseInt("2147483647", 10) 返回 2147483647
     * parseInt("-2147483648", 10) 返回 -2147483648
     * parseInt("2147483648", 10) 抛出 NumberFormatException
     * parseInt("99", 8) 抛出 NumberFormatException
     * parseInt("Kona", 10) 抛出 NumberFormatException
     * parseInt("Kona", 27) 返回 411787
     * </pre></blockquote>
     *
     * @param      s   包含要解析的整数表示形式的 {@code String}
     * @param      radix   解析 {@code s} 时使用的基数。
     * @return     字符串参数在指定基数中表示的整数。
     * @exception  NumberFormatException 如果 {@code String} 不包含可解析的 {@code int}。
     */
    public static int parseInt(String s, int radix)
                throws NumberFormatException
    {
        /*
         * WARNING: This method may be invoked early during VM initialization
         * before IntegerCache is initialized. Care must be taken to not use
         * the valueOf method.
         */

        if (s == null) {
            throw new NumberFormatException("null");
        }

        if (radix < Character.MIN_RADIX) {
            throw new NumberFormatException("radix " + radix +
                                            " less than Character.MIN_RADIX");
        }

        if (radix > Character.MAX_RADIX) {
            throw new NumberFormatException("radix " + radix +
                                            " greater than Character.MAX_RADIX");
        }

        int result = 0;
        boolean negative = false;
        int i = 0, len = s.length();
        int limit = -Integer.MAX_VALUE;
        int multmin;
        int digit;

        if (len > 0) {
            char firstChar = s.charAt(0);
            if (firstChar < '0') { // Possible leading "+" or "-"
                if (firstChar == '-') {
                    negative = true;
                    limit = Integer.MIN_VALUE;
                } else if (firstChar != '+')
                    throw NumberFormatException.forInputString(s);

                if (len == 1) // Cannot have lone "+" or "-"
                    throw NumberFormatException.forInputString(s);
                i++;
            }
            multmin = limit / radix;
            while (i < len) {
                // Accumulating negatively avoids surprises near MAX_VALUE
                digit = Character.digit(s.charAt(i++),radix);
                if (digit < 0) {
                    throw NumberFormatException.forInputString(s);
                }
                if (result < multmin) {
                    throw NumberFormatException.forInputString(s);
                }
                result *= radix;
                if (result < limit + digit) {
                    throw NumberFormatException.forInputString(s);
                }
                result -= digit;
            }
        } else {
            throw NumberFormatException.forInputString(s);
        }
        return negative ? result : -result;
    }

    /**
     * 将字符串参数解析为有符号的十进制整数。字符串中的字符必须都是十进制数字，
     * 除了第一个字符可以是ASCII减号 {@code '-'} ({@code '\u005Cu002D'}) 
     * 来表示负值，或者ASCII加号 {@code '+'} ({@code '\u005Cu002B'}) 
     * 来表示正值。返回结果整数值，就像将参数和基数10作为参数传递给
     * {@link #parseInt(java.lang.String, int)} 方法一样。
     *
     * @param s    包含要解析的 {@code int} 表示的 {@code String}
     * @return     参数以十进制表示的整数值。
     * @exception  NumberFormatException  如果字符串不包含可解析的整数。
     */
    public static int parseInt(String s) throws NumberFormatException {
        return parseInt(s,10);
    }

    /**
     * 将字符串参数解析为第二个参数指定基数的无符号整数。无符号整数将
     * 通常与负数关联的值映射到大于 {@code MAX_VALUE} 的正数。
     *
     * 字符串中的字符必须都是指定基数的数字（由 {@link
     * java.lang.Character#digit(char, int)} 是否返回非负值确定），
     * 除了第一个字符可以是ASCII加号 {@code '+'} ({@code '\u005Cu002B'})。
     * 返回结果整数值。
     *
     * <p>如果发生以下任何情况，将抛出 {@code NumberFormatException} 类型的异常：
     * <ul>
     * <li>第一个参数为 {@code null} 或长度为零的字符串。
     *
     * <li>基数小于 {@link java.lang.Character#MIN_RADIX} 或
     * 大于 {@link java.lang.Character#MAX_RADIX}。
     *
     * <li>字符串的任何字符不是指定基数的数字，除了第一个字符可以是加号
     * {@code '+'} ({@code '\u005Cu002B'})，前提是字符串长度大于1。
     *
     * <li>字符串表示的值大于最大无符号 {@code int}，2<sup>32</sup>-1。
     *
     * </ul>
     *
     *
     * @param      s   包含要解析的无符号整数表示的 {@code String}
     * @param      radix   解析 {@code s} 时要使用的基数。
     * @return     字符串参数在指定基数中表示的整数。
     * @throws     NumberFormatException 如果 {@code String}
     *             不包含可解析的 {@code int}。
     * @since 1.8
     */
    public static int parseUnsignedInt(String s, int radix)
                throws NumberFormatException {
        if (s == null)  {
            throw new NumberFormatException("null");
        }

        int len = s.length();
        if (len > 0) {
            char firstChar = s.charAt(0);
            if (firstChar == '-') {
                throw new
                    NumberFormatException(String.format("Illegal leading minus sign " +
                                                       "on unsigned string %s.", s));
            } else {
                if (len <= 5 || // Integer.MAX_VALUE in Character.MAX_RADIX is 6 digits
                    (radix == 10 && len <= 9) ) { // Integer.MAX_VALUE in base 10 is 10 digits
                    return parseInt(s, radix);
                } else {
                    long ell = Long.parseLong(s, radix);
                    if ((ell & 0xffff_ffff_0000_0000L) == 0) {
                        return (int) ell;
                    } else {
                        throw new
                            NumberFormatException(String.format("String value %s exceeds " +
                                                                "range of unsigned int.", s));
                    }
                }
            }
        } else {
            throw NumberFormatException.forInputString(s);
        }
    }

    /**
     * 将字符串参数解析为无符号的十进制整数。字符串中的字符必须都是十进制数字，
     * 除了第一个字符可以是ASCII加号 {@code '+'} ({@code '\u005Cu002B'})。
     * 返回结果整数值，就像将参数和基数10作为参数传递给
     * {@link #parseUnsignedInt(java.lang.String, int)} 方法一样。
     *
     * @param s   包含要解析的无符号 {@code int} 表示的 {@code String}
     * @return    参数以十进制表示的无符号整数值。
     * @throws    NumberFormatException  如果字符串不包含可解析的无符号整数。
     * @since 1.8
     */
    public static int parseUnsignedInt(String s) throws NumberFormatException {
        return parseUnsignedInt(s, 10);
    }

    /**
     * 返回一个 {@code Integer} 对象，该对象保存从指定 {@code String} 中
     * 提取的值，使用第二个参数给定的基数进行解析。第一个参数被解释为
     * 表示第二个参数指定基数中的有符号整数，就像将参数传递给
     * {@link #parseInt(java.lang.String, int)} 方法一样。
     * 结果是一个表示字符串指定的整数值的 {@code Integer} 对象。
     *
     * <p>换句话说，此方法返回一个等于以下值的 {@code Integer} 对象：
     *
     * <blockquote>
     *  {@code new Integer(Integer.parseInt(s, radix))}
     * </blockquote>
     *
     * @param      s   要解析的字符串。
     * @param      radix 解释 {@code s} 时要使用的基数
     * @return     保存字符串参数在指定基数中表示的值的 {@code Integer} 对象。
     * @exception NumberFormatException 如果 {@code String}
     *            不包含可解析的 {@code int}。
     */
    public static Integer valueOf(String s, int radix) throws NumberFormatException {
        return Integer.valueOf(parseInt(s,radix));
    }

    /**
     * 返回保存指定 {@code String} 值的 {@code Integer} 对象。
     * 参数被解释为表示有符号的十进制整数，就像将参数传递给
     * {@link #parseInt(java.lang.String)} 方法一样。
     * 结果是一个表示字符串指定的整数值的 {@code Integer} 对象。
     *
     * <p>换句话说，此方法返回一个等于以下值的 {@code Integer} 对象：
     *
     * <blockquote>
     *  {@code new Integer(Integer.parseInt(s))}
     * </blockquote>
     *
     * @param      s   要解析的字符串。
     * @return     保存字符串参数表示的值的 {@code Integer} 对象。
     * @exception  NumberFormatException  如果字符串无法解析为整数。
     */
    public static Integer valueOf(String s) throws NumberFormatException {
        return Integer.valueOf(parseInt(s, 10));
    }

    /**
     * Cache to support the object identity semantics of autoboxing for values between
     * -128 and 127 (inclusive) as required by JLS.
     *
     * The cache is initialized on first usage.  The size of the cache
     * may be controlled by the {@code -XX:AutoBoxCacheMax=<size>} option.
     * During VM initialization, java.lang.Integer.IntegerCache.high property
     * may be set and saved in the private system properties in the
     * sun.misc.VM class.
     */

    private static class IntegerCache {
        static final int low = -128;
        static final int high;
        static final Integer cache[];

        static {
            // high value may be configured by property
            int h = 127;
            String integerCacheHighPropValue =
                sun.misc.VM.getSavedProperty("java.lang.Integer.IntegerCache.high");
            if (integerCacheHighPropValue != null) {
                try {
                    int i = parseInt(integerCacheHighPropValue);
                    i = Math.max(i, 127);
                    // Maximum array size is Integer.MAX_VALUE
                    h = Math.min(i, Integer.MAX_VALUE - (-low) -1);
                } catch( NumberFormatException nfe) {
                    // If the property cannot be parsed into an int, ignore it.
                }
            }
            high = h;

            cache = new Integer[(high - low) + 1];
            int j = low;
            for(int k = 0; k < cache.length; k++)
                cache[k] = new Integer(j++);

            // range [-128, 127] must be interned (JLS7 5.1.7)
            assert IntegerCache.high >= 127;
        }

        private IntegerCache() {}
    }

    /**
     * Returns an {@code Integer} instance representing the specified
     * {@code int} value.  If a new {@code Integer} instance is not
     * required, this method should generally be used in preference to
     * the constructor {@link #Integer(int)}, as this method is likely
     * to yield significantly better space and time performance by
     * caching frequently requested values.
     *
     * This method will always cache values in the range -128 to 127,
     * inclusive, and may cache other values outside of this range.
     *
     * @param  i an {@code int} value.
     * @return an {@code Integer} instance representing {@code i}.
     * @since  1.5
     */
    public static Integer valueOf(int i) {
        if (i >= IntegerCache.low && i <= IntegerCache.high)
            return IntegerCache.cache[i + (-IntegerCache.low)];
        return new Integer(i);
    }

    /**
     * The value of the {@code Integer}.
     *
     * @serial
     */
    private final int value;

    /**
     * Constructs a newly allocated {@code Integer} object that
     * represents the specified {@code int} value.
     *
     * @param   value   the value to be represented by the
     *                  {@code Integer} object.
     */
    public Integer(int value) {
        this.value = value;
    }

    /**
     * Constructs a newly allocated {@code Integer} object that
     * represents the {@code int} value indicated by the
     * {@code String} parameter. The string is converted to an
     * {@code int} value in exactly the manner used by the
     * {@code parseInt} method for radix 10.
     *
     * @param      s   the {@code String} to be converted to an
     *                 {@code Integer}.
     * @exception  NumberFormatException  if the {@code String} does not
     *               contain a parsable integer.
     * @see        java.lang.Integer#parseInt(java.lang.String, int)
     */
    public Integer(String s) throws NumberFormatException {
        this.value = parseInt(s, 10);
    }

    /**
     * Returns the value of this {@code Integer} as a {@code byte}
     * after a narrowing primitive conversion.
     * @jls 5.1.3 Narrowing Primitive Conversions
     */
    public byte byteValue() {
        return (byte)value;
    }

    /**
     * Returns the value of this {@code Integer} as a {@code short}
     * after a narrowing primitive conversion.
     * @jls 5.1.3 Narrowing Primitive Conversions
     */
    public short shortValue() {
        return (short)value;
    }

    /**
     * Returns the value of this {@code Integer} as an
     * {@code int}.
     */
    public int intValue() {
        return value;
    }

    /**
     * Returns the value of this {@code Integer} as a {@code long}
     * after a widening primitive conversion.
     * @jls 5.1.2 Widening Primitive Conversions
     * @see Integer#toUnsignedLong(int)
     */
    public long longValue() {
        return (long)value;
    }

    /**
     * Returns the value of this {@code Integer} as a {@code float}
     * after a widening primitive conversion.
     * @jls 5.1.2 Widening Primitive Conversions
     */
    public float floatValue() {
        return (float)value;
    }

    /**
     * Returns the value of this {@code Integer} as a {@code double}
     * after a widening primitive conversion.
     * @jls 5.1.2 Widening Primitive Conversions
     */
    public double doubleValue() {
        return (double)value;
    }

    /**
     * Returns a {@code String} object representing this
     * {@code Integer}'s value. The value is converted to signed
     * decimal representation and returned as a string, exactly as if
     * the integer value were given as an argument to the {@link
     * java.lang.Integer#toString(int)} method.
     *
     * @return  a string representation of the value of this object in
     *          base&nbsp;10.
     */
    public String toString() {
        return toString(value);
    }

    /**
     * Returns a hash code for this {@code Integer}.
     *
     * @return  a hash code value for this object, equal to the
     *          primitive {@code int} value represented by this
     *          {@code Integer} object.
     */
    @Override
    public int hashCode() {
        return Integer.hashCode(value);
    }

    /**
     * 返回 {@code int} 值的哈希码；与 {@code Integer.hashCode()} 兼容。
     *
     * @param value 要哈希的值
     * @since 1.8
     *
     * @return {@code int} 值的哈希码值。
     */
    public static int hashCode(int value) {
        return value;
    }

    /**
     * 将此对象与指定对象比较。当且仅当参数不为 {@code null}
     * 且是一个包含与此对象相同 {@code int} 值的 {@code Integer} 对象时，
     * 结果才为 {@code true}。
     *
     * @param   obj   要比较的对象。
     * @return  如果对象相同则返回 {@code true}；否则返回 {@code false}。
     */
    public boolean equals(Object obj) {
        if (obj instanceof Integer) {
            return value == ((Integer)obj).intValue();
        }
        return false;
    }

    /**
     * 确定具有指定名称的系统属性的整数值。
     *
     * <p>第一个参数被视为系统属性的名称。系统属性可通过
     * {@link java.lang.System#getProperty(java.lang.String)} 方法访问。
     * 然后使用 {@link Integer#decode decode} 支持的语法将此属性的字符串值
     * 解释为整数值，并返回表示此值的 {@code Integer} 对象。
     *
     * <p>如果没有指定名称的属性，如果指定的名称为空或 {@code null}，
     * 或者如果属性没有正确的数字格式，则返回 {@code null}。
     *
     * <p>换句话说，此方法返回一个等于以下值的 {@code Integer} 对象：
     *
     * <blockquote>
     *  {@code getInteger(nm, null)}
     * </blockquote>
     *
     * @param   nm   属性名称。
     * @return  属性的 {@code Integer} 值。
     * @throws  SecurityException 与
     *          {@link System#getProperty(String) System.getProperty} 相同的原因
     * @see     java.lang.System#getProperty(java.lang.String)
     * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
     */
    public static Integer getInteger(String nm) {
        return getInteger(nm, null);
    }

    /**
     * Determines the integer value of the system property with the
     * specified name.
     *
     * <p>The first argument is treated as the name of a system
     * property.  System properties are accessible through the {@link
     * java.lang.System#getProperty(java.lang.String)} method. The
     * string value of this property is then interpreted as an integer
     * value using the grammar supported by {@link Integer#decode decode} and
     * an {@code Integer} object representing this value is returned.
     *
     * <p>The second argument is the default value. An {@code Integer} object
     * that represents the value of the second argument is returned if there
     * is no property of the specified name, if the property does not have
     * the correct numeric format, or if the specified name is empty or
     * {@code null}.
     *
     * <p>In other words, this method returns an {@code Integer} object
     * equal to the value of:
     *
     * <blockquote>
     *  {@code getInteger(nm, new Integer(val))}
     * </blockquote>
     *
     * but in practice it may be implemented in a manner such as:
     *
     * <blockquote><pre>
     * Integer result = getInteger(nm, null);
     * return (result == null) ? new Integer(val) : result;
     * </pre></blockquote>
     *
     * to avoid the unnecessary allocation of an {@code Integer}
     * object when the default value is not needed.
     *
     * @param   nm   property name.
     * @param   val   default value.
     * @return  the {@code Integer} value of the property.
     * @throws  SecurityException for the same reasons as
     *          {@link System#getProperty(String) System.getProperty}
     * @see     java.lang.System#getProperty(java.lang.String)
     * @see     java.lang.System#getProperty(java.lang.String, java.lang.String)
     */
    public static Integer getInteger(String nm, int val) {
        Integer result = getInteger(nm, null);
        return (result == null) ? Integer.valueOf(val) : result;
    }

    /**
     * Returns the integer value of the system property with the
     * specified name.  The first argument is treated as the name of a
     * system property.  System properties are accessible through the
     * {@link java.lang.System#getProperty(java.lang.String)} method.
     * The string value of this property is then interpreted as an
     * integer value, as per the {@link Integer#decode decode} method,
     * and an {@code Integer} object representing this value is
     * returned; in summary:
     *
     * <ul><li>If the property value begins with the two ASCII characters
     *         {@code 0x} or the ASCII character {@code #}, not
     *      followed by a minus sign, then the rest of it is parsed as a
     *      hexadecimal integer exactly as by the method
     *      {@link #valueOf(java.lang.String, int)} with radix 16.
     * <li>If the property value begins with the ASCII character
     *     {@code 0} followed by another character, it is parsed as an
     *     octal integer exactly as by the method
     *     {@link #valueOf(java.lang.String, int)} with radix 8.
     * <li>Otherwise, the property value is parsed as a decimal integer
     * exactly as by the method {@link #valueOf(java.lang.String, int)}
     * with radix 10.
     * </ul>
     *
     * <p>The second argument is the default value. The default value is
     * returned if there is no property of the specified name, if the
     * property does not have the correct numeric format, or if the
     * specified name is empty or {@code null}.
     *
     * @param   nm   property name.
     * @param   val   default value.
     * @return  the {@code Integer} value of the property.
     * @throws  SecurityException for the same reasons as
     *          {@link System#getProperty(String) System.getProperty}
     * @see     System#getProperty(java.lang.String)
     * @see     System#getProperty(java.lang.String, java.lang.String)
     */
    public static Integer getInteger(String nm, Integer val) {
        String v = null;
        try {
            v = System.getProperty(nm);
        } catch (IllegalArgumentException | NullPointerException e) {
        }
        if (v != null) {
            try {
                return Integer.decode(v);
            } catch (NumberFormatException e) {
            }
        }
        return val;
    }

    /**
     * 将 {@code String} 解码为 {@code Integer}。
     * 接受由以下语法给出的十进制、十六进制和八进制数字：
     *
     * <blockquote>
     * <dl>
     * <dt><i>可解码字符串：</i>
     * <dd><i>符号<sub>可选</sub> 十进制数字</i>
     * <dd><i>符号<sub>可选</sub></i> {@code 0x} <i>十六进制数字</i>
     * <dd><i>符号<sub>可选</sub></i> {@code 0X} <i>十六进制数字</i>
     * <dd><i>符号<sub>可选</sub></i> {@code #} <i>十六进制数字</i>
     * <dd><i>符号<sub>可选</sub></i> {@code 0} <i>八进制数字</i>
     *
     * <dt><i>符号：</i>
     * <dd>{@code -}
     * <dd>{@code +}
     * </dl>
     * </blockquote>
     *
     * <i>十进制数字</i>、<i>十六进制数字</i> 和 <i>八进制数字</i>
     * 如 <cite>Java&trade; 语言规范</cite> 第 3.10.1 节中定义，
     * 但数字之间不接受下划线。
     *
     * <p>跟在可选符号和/或基数说明符（"{@code 0x}"、"{@code 0X}"、
     * "{@code #}" 或前导零）后面的字符序列由 {@code Integer.parseInt}
     * 方法使用指示的基数（10、16 或 8）解析。此字符序列必须表示正值，
     * 否则将抛出 {@link NumberFormatException}。如果指定 {@code String}
     * 的第一个字符是减号，则结果取反。{@code String} 中不允许空白字符。
     *
     * @param     nm 要解码的 {@code String}。
     * @return    保存由 {@code nm} 表示的 {@code int} 值的 {@code Integer} 对象
     * @exception NumberFormatException  如果 {@code String} 不包含可解析的整数。
     * @see java.lang.Integer#parseInt(java.lang.String, int)
     */
    public static Integer decode(String nm) throws NumberFormatException {
        int radix = 10;
        int index = 0;
        boolean negative = false;
        Integer result;

        if (nm.isEmpty())
            throw new NumberFormatException("Zero length string");
        char firstChar = nm.charAt(0);
        // Handle sign, if present
        if (firstChar == '-') {
            negative = true;
            index++;
        } else if (firstChar == '+')
            index++;

        // Handle radix specifier, if present
        if (nm.startsWith("0x", index) || nm.startsWith("0X", index)) {
            index += 2;
            radix = 16;
        }
        else if (nm.startsWith("#", index)) {
            index ++;
            radix = 16;
        }
        else if (nm.startsWith("0", index) && nm.length() > 1 + index) {
            index ++;
            radix = 8;
        }

        if (nm.startsWith("-", index) || nm.startsWith("+", index))
            throw new NumberFormatException("Sign character in wrong position");

        try {
            result = Integer.valueOf(nm.substring(index), radix);
            result = negative ? Integer.valueOf(-result.intValue()) : result;
        } catch (NumberFormatException e) {
            // If number is Integer.MIN_VALUE, we'll end up here. The next line
            // handles this case, and causes any genuine format error to be
            // rethrown.
            String constant = negative ? ("-" + nm.substring(index))
                                       : nm.substring(index);
            result = Integer.valueOf(constant, radix);
        }
        return result;
    }

    /**
     * 数值比较两个 {@code Integer} 对象。
     *
     * @param   anotherInteger   要比较的 {@code Integer}。
     * @return  如果此 {@code Integer} 等于参数 {@code Integer}，则返回值 {@code 0}；
     *          如果此 {@code Integer} 在数值上小于参数 {@code Integer}，则返回小于 {@code 0} 的值；
     *          如果此 {@code Integer} 在数值上大于参数 {@code Integer}，则返回大于 {@code 0} 的值
     *          （有符号比较）。
     * @since   1.2
     */
    public int compareTo(Integer anotherInteger) {
        return compare(this.value, anotherInteger.value);
    }

    /**
     * 数值比较两个 {@code int} 值。
     * 返回的值与以下表达式返回的值相同：
     * <pre>
     *    Integer.valueOf(x).compareTo(Integer.valueOf(y))
     * </pre>
     *
     * @param  x 要比较的第一个 {@code int}
     * @param  y 要比较的第二个 {@code int}
     * @return 如果 {@code x == y}，则返回值 {@code 0}；
     *         如果 {@code x < y}，则返回小于 {@code 0} 的值；
     *         如果 {@code x > y}，则返回大于 {@code 0} 的值
     * @since 1.7
     */
    public static int compare(int x, int y) {
        return (x < y) ? -1 : ((x == y) ? 0 : 1);
    }

    /**
     * 将值作为无符号值处理，数值比较两个 {@code int} 值。
     *
     * @param  x 要比较的第一个 {@code int}
     * @param  y 要比较的第二个 {@code int}
     * @return 如果 {@code x == y}，则返回值 {@code 0}；
     *         如果作为无符号值 {@code x < y}，则返回小于 {@code 0} 的值；
     *         如果作为无符号值 {@code x > y}，则返回大于 {@code 0} 的值
     * @since 1.8
     */
    public static int compareUnsigned(int x, int y) {
        return compare(x + MIN_VALUE, y + MIN_VALUE);
    }

    /**
     * 通过无符号转换将参数转换为 {@code long}。在到 {@code long} 的无符号转换中，
     * {@code long} 的高位 32 位为零，低位 32 位等于整数参数的位。
     *
     * 因此，零和正 {@code int} 值映射到数值相等的 {@code long} 值，
     * 负 {@code int} 值映射到等于输入加 2<sup>32</sup> 的 {@code long} 值。
     *
     * @param  x 要转换为无符号 {@code long} 的值
     * @return 通过无符号转换将参数转换为 {@code long}
     * @since 1.8
     */
    public static long toUnsignedLong(int x) {
        return ((long) x) & 0xffffffffL;
    }

    /**
     * Returns the unsigned quotient of dividing the first argument by
     * the second where each argument and the result is interpreted as
     * an unsigned value.
     *
     * <p>Note that in two's complement arithmetic, the three other
     * basic arithmetic operations of add, subtract, and multiply are
     * bit-wise identical if the two operands are regarded as both
     * being signed or both being unsigned.  Therefore separate {@code
     * addUnsigned}, etc. methods are not provided.
     *
     * @param dividend the value to be divided
     * @param divisor the value doing the dividing
     * @return the unsigned quotient of the first argument divided by
     * the second argument
     * @see #remainderUnsigned
     * @since 1.8
     */
    public static int divideUnsigned(int dividend, int divisor) {
        // In lieu of tricky code, for now just use long arithmetic.
        return (int)(toUnsignedLong(dividend) / toUnsignedLong(divisor));
    }

    /**
     * Returns the unsigned remainder from dividing the first argument
     * by the second where each argument and the result is interpreted
     * as an unsigned value.
     *
     * @param dividend the value to be divided
     * @param divisor the value doing the dividing
     * @return the unsigned remainder of the first argument divided by
     * the second argument
     * @see #divideUnsigned
     * @since 1.8
     */
    public static int remainderUnsigned(int dividend, int divisor) {
        // In lieu of tricky code, for now just use long arithmetic.
        return (int)(toUnsignedLong(dividend) % toUnsignedLong(divisor));
    }


    // Bit twiddling

    /**
     * The number of bits used to represent an {@code int} value in two's
     * complement binary form.
     *
     * @since 1.5
     */
    @Native public static final int SIZE = 32;

    /**
     * The number of bytes used to represent a {@code int} value in two's
     * complement binary form.
     *
     * @since 1.8
     */
    public static final int BYTES = SIZE / Byte.SIZE;

    /**
     * Returns an {@code int} value with at most a single one-bit, in the
     * position of the highest-order ("leftmost") one-bit in the specified
     * {@code int} value.  Returns zero if the specified value has no
     * one-bits in its two's complement binary representation, that is, if it
     * is equal to zero.
     *
     * @param i the value whose highest one bit is to be computed
     * @return an {@code int} value with a single one-bit, in the position
     *     of the highest-order one-bit in the specified value, or zero if
     *     the specified value is itself equal to zero.
     * @since 1.5
     */
    public static int highestOneBit(int i) {
        // HD, Figure 3-1
        i |= (i >>  1);
        i |= (i >>  2);
        i |= (i >>  4);
        i |= (i >>  8);
        i |= (i >> 16);
        return i - (i >>> 1);
    }

    /**
     * Returns an {@code int} value with at most a single one-bit, in the
     * position of the lowest-order ("rightmost") one-bit in the specified
     * {@code int} value.  Returns zero if the specified value has no
     * one-bits in its two's complement binary representation, that is, if it
     * is equal to zero.
     *
     * @param i the value whose lowest one bit is to be computed
     * @return an {@code int} value with a single one-bit, in the position
     *     of the lowest-order one-bit in the specified value, or zero if
     *     the specified value is itself equal to zero.
     * @since 1.5
     */
    public static int lowestOneBit(int i) {
        // HD, Section 2-1
        return i & -i;
    }

    /**
     * Returns the number of zero bits preceding the highest-order
     * ("leftmost") one-bit in the two's complement binary representation
     * of the specified {@code int} value.  Returns 32 if the
     * specified value has no one-bits in its two's complement representation,
     * in other words if it is equal to zero.
     *
     * <p>Note that this method is closely related to the logarithm base 2.
     * For all positive {@code int} values x:
     * <ul>
     * <li>floor(log<sub>2</sub>(x)) = {@code 31 - numberOfLeadingZeros(x)}
     * <li>ceil(log<sub>2</sub>(x)) = {@code 32 - numberOfLeadingZeros(x - 1)}
     * </ul>
     *
     * @param i the value whose number of leading zeros is to be computed
     * @return the number of zero bits preceding the highest-order
     *     ("leftmost") one-bit in the two's complement binary representation
     *     of the specified {@code int} value, or 32 if the value
     *     is equal to zero.
     * @since 1.5
     */
    public static int numberOfLeadingZeros(int i) {
        // HD, Figure 5-6
        if (i == 0)
            return 32;
        int n = 1;
        if (i >>> 16 == 0) { n += 16; i <<= 16; }
        if (i >>> 24 == 0) { n +=  8; i <<=  8; }
        if (i >>> 28 == 0) { n +=  4; i <<=  4; }
        if (i >>> 30 == 0) { n +=  2; i <<=  2; }
        n -= i >>> 31;
        return n;
    }

    /**
     * Returns the number of zero bits following the lowest-order ("rightmost")
     * one-bit in the two's complement binary representation of the specified
     * {@code int} value.  Returns 32 if the specified value has no
     * one-bits in its two's complement representation, in other words if it is
     * equal to zero.
     *
     * @param i the value whose number of trailing zeros is to be computed
     * @return the number of zero bits following the lowest-order ("rightmost")
     *     one-bit in the two's complement binary representation of the
     *     specified {@code int} value, or 32 if the value is equal
     *     to zero.
     * @since 1.5
     */
    public static int numberOfTrailingZeros(int i) {
        // HD, Figure 5-14
        int y;
        if (i == 0) return 32;
        int n = 31;
        y = i <<16; if (y != 0) { n = n -16; i = y; }
        y = i << 8; if (y != 0) { n = n - 8; i = y; }
        y = i << 4; if (y != 0) { n = n - 4; i = y; }
        y = i << 2; if (y != 0) { n = n - 2; i = y; }
        return n - ((i << 1) >>> 31);
    }

    /**
     * Returns the number of one-bits in the two's complement binary
     * representation of the specified {@code int} value.  This function is
     * sometimes referred to as the <i>population count</i>.
     *
     * @param i the value whose bits are to be counted
     * @return the number of one-bits in the two's complement binary
     *     representation of the specified {@code int} value.
     * @since 1.5
     */
    public static int bitCount(int i) {
        // HD, Figure 5-2
        i = i - ((i >>> 1) & 0x55555555);
        i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
        i = (i + (i >>> 4)) & 0x0f0f0f0f;
        i = i + (i >>> 8);
        i = i + (i >>> 16);
        return i & 0x3f;
    }

    /**
     * Returns the value obtained by rotating the two's complement binary
     * representation of the specified {@code int} value left by the
     * specified number of bits.  (Bits shifted out of the left hand, or
     * high-order, side reenter on the right, or low-order.)
     *
     * <p>Note that left rotation with a negative distance is equivalent to
     * right rotation: {@code rotateLeft(val, -distance) == rotateRight(val,
     * distance)}.  Note also that rotation by any multiple of 32 is a
     * no-op, so all but the last five bits of the rotation distance can be
     * ignored, even if the distance is negative: {@code rotateLeft(val,
     * distance) == rotateLeft(val, distance & 0x1F)}.
     *
     * @param i the value whose bits are to be rotated left
     * @param distance the number of bit positions to rotate left
     * @return the value obtained by rotating the two's complement binary
     *     representation of the specified {@code int} value left by the
     *     specified number of bits.
     * @since 1.5
     */
    public static int rotateLeft(int i, int distance) {
        return (i << distance) | (i >>> -distance);
    }

    /**
     * Returns the value obtained by rotating the two's complement binary
     * representation of the specified {@code int} value right by the
     * specified number of bits.  (Bits shifted out of the right hand, or
     * low-order, side reenter on the left, or high-order.)
     *
     * <p>Note that right rotation with a negative distance is equivalent to
     * left rotation: {@code rotateRight(val, -distance) == rotateLeft(val,
     * distance)}.  Note also that rotation by any multiple of 32 is a
     * no-op, so all but the last five bits of the rotation distance can be
     * ignored, even if the distance is negative: {@code rotateRight(val,
     * distance) == rotateRight(val, distance & 0x1F)}.
     *
     * @param i the value whose bits are to be rotated right
     * @param distance the number of bit positions to rotate right
     * @return the value obtained by rotating the two's complement binary
     *     representation of the specified {@code int} value right by the
     *     specified number of bits.
     * @since 1.5
     */
    public static int rotateRight(int i, int distance) {
        return (i >>> distance) | (i << -distance);
    }

    /**
     * Returns the value obtained by reversing the order of the bits in the
     * two's complement binary representation of the specified {@code int}
     * value.
     *
     * @param i the value to be reversed
     * @return the value obtained by reversing order of the bits in the
     *     specified {@code int} value.
     * @since 1.5
     */
    public static int reverse(int i) {
        // HD, Figure 7-1
        i = (i & 0x55555555) << 1 | (i >>> 1) & 0x55555555;
        i = (i & 0x33333333) << 2 | (i >>> 2) & 0x33333333;
        i = (i & 0x0f0f0f0f) << 4 | (i >>> 4) & 0x0f0f0f0f;
        i = (i << 24) | ((i & 0xff00) << 8) |
            ((i >>> 8) & 0xff00) | (i >>> 24);
        return i;
    }

    /**
     * Returns the signum function of the specified {@code int} value.  (The
     * return value is -1 if the specified value is negative; 0 if the
     * specified value is zero; and 1 if the specified value is positive.)
     *
     * @param i the value whose signum is to be computed
     * @return the signum function of the specified {@code int} value.
     * @since 1.5
     */
    public static int signum(int i) {
        // HD, Section 2-7
        return (i >> 31) | (-i >>> 31);
    }

    /**
     * Returns the value obtained by reversing the order of the bytes in the
     * two's complement representation of the specified {@code int} value.
     *
     * @param i the value whose bytes are to be reversed
     * @return the value obtained by reversing the bytes in the specified
     *     {@code int} value.
     * @since 1.5
     */
    public static int reverseBytes(int i) {
        return ((i >>> 24)           ) |
               ((i >>   8) &   0xFF00) |
               ((i <<   8) & 0xFF0000) |
               ((i << 24));
    }

    /**
     * Adds two integers together as per the + operator.
     *
     * @param a the first operand
     * @param b the second operand
     * @return the sum of {@code a} and {@code b}
     * @see java.util.function.BinaryOperator
     * @since 1.8
     */
    public static int sum(int a, int b) {
        return a + b;
    }

    /**
     * Returns the greater of two {@code int} values
     * as if by calling {@link Math#max(int, int) Math.max}.
     *
     * @param a the first operand
     * @param b the second operand
     * @return the greater of {@code a} and {@code b}
     * @see java.util.function.BinaryOperator
     * @since 1.8
     */
    public static int max(int a, int b) {
        return Math.max(a, b);
    }

    /**
     * Returns the smaller of two {@code int} values
     * as if by calling {@link Math#min(int, int) Math.min}.
     *
     * @param a the first operand
     * @param b the second operand
     * @return the smaller of {@code a} and {@code b}
     * @see java.util.function.BinaryOperator
     * @since 1.8
     */
    public static int min(int a, int b) {
        return Math.min(a, b);
    }

    /** use serialVersionUID from JDK 1.0.2 for interoperability */
    @Native private static final long serialVersionUID = 1360826667806852920L;
}
